Software Security The following give the number of bits in an encryption key. Fo
ID: 3670066 • Letter: S
Question
Software Security
The following give the number of bits in an encryption key. For each, calculate the number of trials it will take to crack that key, approximately in powers of ten (10). Also calculate the average time required to crack that key assuming we can perform 10 million attempts per second. Be sure to use time units (days or years) that are reasonably close to the cracking time, or in years if the time takes more than a year.
(e.g.) 70 bits
the number of trials to crack the key: 270 = 1.18 x 1021 1021 trials would be needed
Can perform 10 million (107) attempts per second, so to crack the key, it will take 1021 / 107 seconds = 1014 seconds
1 year = 60 x 60 x 24 x 365 = 31536000 seconds 3 x 107
1014 / (3 x 107) = 107 / 3 3.333 x 106 or 3,333,333 years to crack the key
a. 40 bits
b. 56 bits
c. 64 bits
d. 80 bits
e. 128 bits
f. 256 bits
Explanation / Answer
a) 40 bits
number of trials to crack the key: 240 = 1.099511628×10¹² 1012
10 million (107) attempts per second
It will take 1012 / 107 seconds = 105 seconds
1 year 3 x 107
Total year required to break = 105/3 x 107 = 3.333x 10-3 =3.333x 10-3 x 365 days = 1.2 days to crack the key
b) 56 bits
number of trials to crack the key: 256 = 7.205759404×10¹² 1016
10 million (107) attempts per second
It will take 1016 / 107 seconds = 109 seconds
1 year 3 x 107
Total year required to break = 109/3 x 107 = 3.333x 10 = 33 years to crack the key
c) 64 bits
number of trials to crack the key: 264 = 1.844674407×10¹ 1019
10 million (107) attempts per second
It will take 1019 / 107 seconds = 1011 seconds
1 year 3 x 107
Total year required to break = 1011/3 x 107 = 3.333x 103 = 3,333 years to crack the key
d) 80 bits
number of trials to crack the key: 280 = 1.20892582×10² 1024
10 million (107) attempts per second
It will take 1024 / 107 seconds = 1017 seconds
1 year 3 x 107
Total year required to break = 1017/3 x 107 = 3.333x 109 = 3,333,333,333 years to crack the key
e) 128 bits
number of trials to crack the key: 280 =3.402823669×10³ 1038
10 million (107) attempts per second
It will take 1038 / 107 seconds = 1031 seconds
1 year 3 x 107
Total year required to break = 1031/3 x 107 = 3.333x 1023 = 33,333,333,333,333,333,333,333years to crack the key
f)256 bits
number of trials to crack the key: 280 =1.157920892×10 1077
10 million (107) attempts per second
It will take 1077 / 107 seconds = 1070 seconds
1 year 3 x 107
Total year required to break = 1070/3 x 107 = 3.333x 1062 = 3,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333 years to crack the key
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.